Often the first thing a non-photographer will notice about one of our images is the sharp subject in the foreground with a blurry background. If you're shooting with what we call a 'point and shoot' camera it can be difficult to achieve this, but with a dSLR you can create the background blur (called bokeh) quite simply.
If you're just starting out, try your hand with the 'A' mode on your dSLR. That's A for aperture, not auto!
Aperture is how wide the shutter will open when you take a shot. The wider the aperture, the more light that is let into the lens and the shallower your depth of field. A shallow depth of field is what will give you nice smooth bokeh.
The diagram below gives a better illustration of how depth of field works that we can explain with words.
As you can see from the diagram, if your aperture is wide open (at f/2.8), the depth of field (the part of the picture that will be in focus, i.e. the grey highlighted part in the diagram) will be relatively small. At f/11, a much larger part of the image will be in focus.
The smaller your aperture (some dSLRs go up to f/32), the more of your image will be in focus. The larger your aperture, the blurrier your background will be (shallower depth of field).
While the bokeh effect can make for beautiful photos, it can also hinder your attempts to take sharp photos. Because the depth of field can be so shallow at wider apertures, particularly when shooting a subject up close, it's very easy for things to fall outside the focus area. If you're having trouble getting the parts of your image in focus that you want sharp, try reducing your aperture (smaller hole, bigger number - f/10 is a good starting point if you have a group of people). Experiment with different f-stops until you get the effect you want. That's the beauty of digital!